LMFDB - Embedded newform 234.4.l.b.127.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [234,4,Mod(127,234)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(234, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 5]))

N = Newforms(chi, 4, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("234.127");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 234 = 2 \cdot 3^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	234.l (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$13.8064469413$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{8} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} + 122x^{6} + 5305x^{4} + 97056x^{2} + 627264 $ x^8 + 122x^6 + 5305x^4 + 97056*x^2 + 627264
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 2^{4} $
Twist minimal:	no (minimal twist has level 26)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			127.1
Root			$-6.87513i$ of defining polynomial
Character	$\chi$	$=$	234.127
Dual form			234.4.l.b.199.2

$q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.73205 + 1.00000i) q^{2} +(2.00000 - 3.46410i) q^{4} -3.30629i q^{5} +(27.1849 + 15.6952i) q^{7} +8.00000i q^{8} +O(q^{10})$	\(q+(-1.73205 + 1.00000i) q^{2} +(2.00000 - 3.46410i) q^{4} -3.30629i q^{5} +(27.1849 + 15.6952i) q^{7} +8.00000i q^{8} +(3.30629 + 5.72666i) q^{10} +(-13.5192 + 7.80533i) q^{11} +(-45.2497 - 12.2255i) q^{13} -62.7808 q^{14} +(-8.00000 - 13.8564i) q^{16} +(53.8638 - 93.2949i) q^{17} +(52.6358 + 30.3893i) q^{19} +(-11.4533 - 6.61258i) q^{20} +(15.6107 - 27.0385i) q^{22} +(62.1540 + 107.654i) q^{23} +114.068 q^{25} +(90.6003 - 24.0746i) q^{26} +(108.740 - 62.7808i) q^{28} +(29.1001 + 50.4028i) q^{29} +200.934i q^{31} +(27.7128 + 16.0000i) q^{32} +215.455i q^{34} +(51.8928 - 89.8810i) q^{35} +(-90.9447 + 52.5069i) q^{37} -121.557 q^{38} +26.4503 q^{40} +(191.461 - 110.540i) q^{41} +(56.0339 - 97.0535i) q^{43} +62.4426i q^{44} +(-215.308 - 124.308i) q^{46} +512.102i q^{47} +(321.178 + 556.297i) q^{49} +(-197.572 + 114.068i) q^{50} +(-132.850 + 132.299i) q^{52} +221.755 q^{53} +(25.8067 + 44.6985i) q^{55} +(-125.562 + 217.479i) q^{56} +(-100.806 - 58.2002i) q^{58} +(482.310 + 278.462i) q^{59} +(229.105 - 396.821i) q^{61} +(-200.934 - 348.028i) q^{62} -64.0000 q^{64} +(-40.4209 + 149.609i) q^{65} +(458.769 - 264.870i) q^{67} +(-215.455 - 373.180i) q^{68} +207.571i q^{70} +(-58.5007 - 33.7754i) q^{71} +104.504i q^{73} +(105.014 - 181.889i) q^{74} +(210.543 - 121.557i) q^{76} -490.025 q^{77} +611.085 q^{79} +(-45.8133 + 26.4503i) q^{80} +(-221.080 + 382.922i) q^{82} -491.565i q^{83} +(-308.460 - 178.089i) q^{85} +224.136i q^{86} +(-62.4426 - 108.154i) q^{88} +(-326.626 + 188.578i) q^{89} +(-1038.23 - 1042.55i) q^{91} +497.232 q^{92} +(-512.102 - 886.987i) q^{94} +(100.476 - 174.029i) q^{95} +(-496.503 - 286.656i) q^{97} +(-1112.59 - 642.357i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 16 q^{4} + 18 q^{7}+O(q^{10}) $ 8 * q + 16 * q^4 + 18 * q^7	$ 8 q + 16 q^{4} + 18 q^{7} - 8 q^{10} + 18 q^{11} - 130 q^{13} - 80 q^{14} - 64 q^{16} - 112 q^{17} + 594 q^{19} - 72 q^{20} - 72 q^{22} + 230 q^{23} - 180 q^{25} + 184 q^{26} + 72 q^{28} - 32 q^{29} + 128 q^{35} - 768 q^{37} + 576 q^{38} - 64 q^{40} + 564 q^{41} - 114 q^{43} + 576 q^{46} - 110 q^{49} - 1968 q^{50} - 104 q^{52} - 36 q^{53} + 1248 q^{55} - 160 q^{56} - 1848 q^{58} + 1110 q^{59} + 900 q^{61} - 1064 q^{62} - 512 q^{64} - 1870 q^{65} + 510 q^{67} + 448 q^{68} + 1470 q^{71} + 680 q^{74} + 2376 q^{76} - 2340 q^{77} + 784 q^{79} - 288 q^{80} + 704 q^{82} - 2898 q^{85} + 288 q^{88} + 4434 q^{89} - 886 q^{91} + 1840 q^{92} - 2568 q^{94} + 816 q^{95} + 1854 q^{97} - 4272 q^{98}+O(q^{100}) $ 8 * q + 16 * q^4 + 18 * q^7 - 8 * q^10 + 18 * q^11 - 130 * q^13 - 80 * q^14 - 64 * q^16 - 112 * q^17 + 594 * q^19 - 72 * q^20 - 72 * q^22 + 230 * q^23 - 180 * q^25 + 184 * q^26 + 72 * q^28 - 32 * q^29 + 128 * q^35 - 768 * q^37 + 576 * q^38 - 64 * q^40 + 564 * q^41 - 114 * q^43 + 576 * q^46 - 110 * q^49 - 1968 * q^50 - 104 * q^52 - 36 * q^53 + 1248 * q^55 - 160 * q^56 - 1848 * q^58 + 1110 * q^59 + 900 * q^61 - 1064 * q^62 - 512 * q^64 - 1870 * q^65 + 510 * q^67 + 448 * q^68 + 1470 * q^71 + 680 * q^74 + 2376 * q^76 - 2340 * q^77 + 784 * q^79 - 288 * q^80 + 704 * q^82 - 2898 * q^85 + 288 * q^88 + 4434 * q^89 - 886 * q^91 + 1840 * q^92 - 2568 * q^94 + 816 * q^95 + 1854 * q^97 - 4272 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/234\mathbb{Z}\right)^\times$.

$n$	$145$	$209$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−1.73205	+	1.00000i	−0.612372	+	0.353553i
$2$	−1.73205	+	1.00000i	−0.612372	+	0.353553i
$3$		0			0
$3$		0			0
$4$	2.00000	−	3.46410i	0.250000	−	0.433013i
$5$		−	3.30629i		−	0.295723i	−0.989008	−	0.147862i	$-0.952761\pi$
$5$		−	3.30629i		−	0.295723i	0.989008	−	0.147862i	$-0.0472390\pi$
$6$		0			0
$7$	27.1849	+	15.6952i	1.46785	+	0.847461i	0.999352	−	0.0360059i	$-0.0114635\pi$
$7$	27.1849	+	15.6952i	1.46785	+	0.847461i	0.468494	+	0.883467i	$0.344797\pi$
$8$			8.00000i			0.353553i
$9$		0			0
$10$	3.30629	+	5.72666i	0.104554	+	0.181093i
$11$	−13.5192	+	7.80533i	−0.370564	+	0.213945i	−0.673705	−	0.739001i	$-0.735298\pi$
$11$	−13.5192	+	7.80533i	−0.370564	+	0.213945i	0.303141	+	0.952946i	$0.401965\pi$
$12$		0			0
$13$	−45.2497	−	12.2255i	−0.965386	−	0.260826i
$13$	−45.2497	−	12.2255i	−0.965386	−	0.260826i
$14$	−62.7808			−1.19849
$15$		0			0
$16$	−8.00000	−	13.8564i	−0.125000	−	0.216506i
$17$	53.8638	−	93.2949i	0.768465	−	1.33102i	−0.169930	−	0.985456i	$-0.554354\pi$
$17$	53.8638	−	93.2949i	0.768465	−	1.33102i	0.938395	−	0.345564i	$-0.112312\pi$
$18$		0			0
$19$	52.6358	+	30.3893i	0.635551	+	0.366936i	0.782899	−	0.622149i	$-0.213740\pi$
$19$	52.6358	+	30.3893i	0.635551	+	0.366936i	−0.147347	+	0.989085i	$0.547074\pi$
$20$	−11.4533	−	6.61258i	−0.128052	−	0.0739308i
$21$		0			0
$22$	15.6107	−	27.0385i	0.151282	−	0.262028i
$23$	62.1540	+	107.654i	0.563479	+	0.975974i	0.997189	+	0.0749214i	$0.0238706\pi$
$23$	62.1540	+	107.654i	0.563479	+	0.975974i	−0.433711	+	0.901052i	$0.642796\pi$
$24$		0			0
$25$	114.068			0.912548
$26$	90.6003	−	24.0746i	0.683392	−	0.181593i
$27$		0			0
$28$	108.740	−	62.7808i	0.733923	−	0.423730i
$29$	29.1001	+	50.4028i	0.186336	+	0.322744i	0.944026	−	0.329871i	$-0.107005\pi$
$29$	29.1001	+	50.4028i	0.186336	+	0.322744i	−0.757690	+	0.652615i	$0.773672\pi$
$30$		0			0
$31$			200.934i			1.16416i	0.813133	+	0.582078i	$0.197760\pi$
$31$			200.934i			1.16416i	−0.813133	+	0.582078i	$0.802240\pi$
$32$	27.7128	+	16.0000i	0.153093	+	0.0883883i
$33$		0			0
$34$			215.455i			1.08677i
$35$	51.8928	−	89.8810i	0.250614	−	0.434076i
$36$		0			0
$37$	−90.9447	+	52.5069i	−0.404087	+	0.233300i	−0.688246	−	0.725478i	$-0.741619\pi$
$37$	−90.9447	+	52.5069i	−0.404087	+	0.233300i	0.284159	+	0.958777i	$0.408286\pi$
$38$	−121.557			−0.518926
$39$		0			0
$40$	26.4503			0.104554
$41$	191.461	−	110.540i	0.729298	−	0.421060i	−0.0888675	−	0.996043i	$-0.528325\pi$
$41$	191.461	−	110.540i	0.729298	−	0.421060i	0.818165	+	0.574983i	$0.194991\pi$
$42$		0			0
$43$	56.0339	−	97.0535i	0.198723	−	0.344198i	−0.749392	−	0.662127i	$-0.769654\pi$
$43$	56.0339	−	97.0535i	0.198723	−	0.344198i	0.948115	+	0.317929i	$0.102987\pi$
$44$			62.4426i			0.213945i
$45$		0			0
$46$	−215.308	−	124.308i	−0.690117	−	0.398440i
$47$			512.102i			1.58931i	0.607058	+	0.794657i	$0.292349\pi$
$47$			512.102i			1.58931i	−0.607058	+	0.794657i	$0.707651\pi$
$48$		0			0
$49$	321.178	+	556.297i	0.936380	+	1.62186i
$50$	−197.572	+	114.068i	−0.558819	+	0.322634i
$51$		0			0
$52$	−132.850	+	132.299i	−0.354287	+	0.352818i
$53$	221.755			0.574724			0.287362	−	0.957822i	$-0.407222\pi$
$53$	221.755			0.574724			0.287362	+	0.957822i	$0.407222\pi$
$54$		0			0
$55$	25.8067	+	44.6985i	0.0632686	+	0.109584i
$56$	−125.562	+	217.479i	−0.299623	+	0.518962i
$57$		0			0
$58$	−100.806	−	58.2002i	−0.228214	−	0.131760i
$59$	482.310	+	278.462i	1.06426	+	0.614452i	0.926608	−	0.376028i	$-0.122710\pi$
$59$	482.310	+	278.462i	1.06426	+	0.614452i	0.137654	+	0.990480i	$0.456044\pi$
$60$		0			0
$61$	229.105	−	396.821i	0.480882	−	0.832913i	−0.518877	−	0.854849i	$-0.673650\pi$
$61$	229.105	−	396.821i	0.480882	−	0.832913i	0.999759	+	0.0219361i	$0.00698304\pi$
$62$	−200.934	−	348.028i	−0.411591	−	0.712897i
$63$		0			0
$64$	−64.0000			−0.125000
$65$	−40.4209	+	149.609i	−0.0771323	+	0.285487i
$66$		0			0
$67$	458.769	−	264.870i	0.836530	−	0.482971i	−0.0195533	−	0.999809i	$-0.506224\pi$
$67$	458.769	−	264.870i	0.836530	−	0.482971i	0.856083	+	0.516838i	$0.172891\pi$
$68$	−215.455	−	373.180i	−0.384232	−	0.665510i
$69$		0			0
$70$			207.571i			0.354422i
$71$	−58.5007	−	33.7754i	−0.0977854	−	0.0564564i	0.450310	−	0.892872i	$-0.351314\pi$
$71$	−58.5007	−	33.7754i	−0.0977854	−	0.0564564i	−0.548095	+	0.836416i	$0.684647\pi$
$72$		0			0
$73$			104.504i			0.167552i	0.996485	+	0.0837759i	$0.0266980\pi$
$73$			104.504i			0.167552i	−0.996485	+	0.0837759i	$0.973302\pi$
$74$	105.014	−	181.889i	0.164968	−	0.285732i
$75$		0			0
$76$	210.543	−	121.557i	0.317776	−	0.183468i
$77$	−490.025			−0.725240
$78$		0			0
$79$	611.085			0.870284			0.435142	−	0.900362i	$-0.356698\pi$
$79$	611.085			0.870284			0.435142	+	0.900362i	$0.356698\pi$
$80$	−45.8133	+	26.4503i	−0.0640260	+	0.0369654i
$81$		0			0
$82$	−221.080	+	382.922i	−0.297735	+	0.515691i
$83$		−	491.565i		−	0.650075i	−0.945701	−	0.325038i	$-0.894623\pi$
$83$		−	491.565i		−	0.650075i	0.945701	−	0.325038i	$-0.105377\pi$
$84$		0			0
$85$	−308.460	−	178.089i	−0.393614	−	0.227253i
$86$			224.136i			0.281037i
$87$		0			0
$88$	−62.4426	−	108.154i	−0.0756410	−	0.131014i
$89$	−326.626	+	188.578i	−0.389014	+	0.224598i	−0.681733	−	0.731601i	$-0.738773\pi$
$89$	−326.626	+	188.578i	−0.389014	+	0.224598i	0.292719	+	0.956199i	$0.405440\pi$
$90$		0			0
$91$	−1038.23	−	1042.55i	−1.19600	−	1.20098i
$92$	497.232			0.563479
$93$		0			0
$94$	−512.102	−	886.987i	−0.561908	−	0.973252i
$95$	100.476	−	174.029i	0.108511	−	0.187947i
$96$		0			0
$97$	−496.503	−	286.656i	−0.519713	−	0.300057i	0.217104	−	0.976148i	$-0.430339\pi$
$97$	−496.503	−	286.656i	−0.519713	−	0.300057i	−0.736817	+	0.676092i	$0.763672\pi$
$98$	−1112.59	−	642.357i	−1.14683	−	0.662121i
$99$		0			0
$100$	228.137	−	395.145i	0.228137	−	0.395145i
$101$	−477.751	−	827.489i	−0.470673	−	0.815230i	0.528764	−	0.848769i	$-0.322656\pi$
$101$	−477.751	−	827.489i	−0.470673	−	0.815230i	−0.999437	+	0.0335385i	$0.989322\pi$
$102$		0			0
$103$	−1478.96			−1.41481			−0.707407	−	0.706806i	$-0.750135\pi$
$103$	−1478.96			−1.41481			−0.707407	+	0.706806i	$0.750135\pi$
$104$	97.8037	−	361.998i	0.0922158	−	0.341315i
$105$		0			0
$106$	−384.091	+	221.755i	−0.351945	+	0.203196i
$107$	106.558	+	184.564i	0.0962741	+	0.166752i	0.910140	−	0.414302i	$-0.135974\pi$
$107$	106.558	+	184.564i	0.0962741	+	0.166752i	−0.813866	+	0.581053i	$0.802641\pi$
$108$		0			0
$109$			84.4197i			0.0741829i	0.999312	+	0.0370915i	$0.0118093\pi$
$109$			84.4197i			0.0741829i	−0.999312	+	0.0370915i	$0.988191\pi$
$110$	−89.3969	−	51.6133i	−0.0774878	−	0.0447376i
$111$		0			0
$112$		−	502.246i		−	0.423730i
$113$	−393.209	+	681.058i	−0.327345	+	0.566979i	−0.981984	−	0.188963i	$-0.939487\pi$
$113$	−393.209	+	681.058i	−0.327345	+	0.566979i	0.654639	+	0.755942i	$0.272821\pi$
$114$		0			0
$115$	355.935	−	205.499i	0.288618	−	0.166634i
$116$	232.801			0.186336
$117$		0			0
$118$	−1113.85			−0.868966
$119$	2928.56	−	1690.81i	2.25598	−	1.30249i
$120$		0			0
$121$	−543.654	+	941.636i	−0.408455	+	0.707465i
$122$			916.418i			0.680070i
$123$		0			0
$124$	696.056	+	401.868i	0.504094	+	0.291039i
$125$		−	790.429i		−	0.565585i
$126$		0			0
$127$	−366.227	−	634.324i	−0.255885	−	0.443206i	0.709250	−	0.704957i	$-0.249034\pi$
$127$	−366.227	−	634.324i	−0.255885	−	0.443206i	−0.965136	+	0.261750i	$0.915700\pi$
$128$	110.851	−	64.0000i	0.0765466	−	0.0441942i
$129$		0			0
$130$	−79.5975	−	299.551i	−0.0537013	−	0.202095i
$131$	−1862.41			−1.24213			−0.621066	−	0.783758i	$-0.713300\pi$
$131$	−1862.41			−1.24213			−0.621066	+	0.783758i	$0.713300\pi$
$132$		0			0
$133$	953.932	+	1652.26i	0.621927	+	1.07721i
$134$	−529.740	+	917.537i	−0.341512	+	0.591516i
$135$		0			0
$136$	746.359	+	430.911i	0.470587	+	0.271693i
$137$	768.559	+	443.728i	0.479288	+	0.276717i	0.720120	−	0.693850i	$-0.244087\pi$
$137$	768.559	+	443.728i	0.479288	+	0.276717i	−0.240832	+	0.970567i	$0.577420\pi$
$138$		0			0
$139$	726.060	−	1257.57i	0.443047	−	0.767381i	−0.554867	−	0.831939i	$-0.687231\pi$
$139$	726.060	−	1257.57i	0.443047	−	0.767381i	0.997914	+	0.0645588i	$0.0205640\pi$
$140$	−207.571	−	359.524i	−0.125307	−	0.217038i
$141$		0			0
$142$	135.102			0.0798414
$143$	707.165	−	187.910i	0.413539	−	0.109887i
$144$		0			0
$145$	166.646	−	96.2133i	0.0954429	−	0.0551040i
$146$	−104.504	−	181.007i	−0.0592385	−	0.102604i
$147$		0			0
$148$			420.055i			0.233300i
$149$	−1336.02	−	771.351i	−0.734570	−	0.424104i	0.0855217	−	0.996336i	$-0.472744\pi$
$149$	−1336.02	−	771.351i	−0.734570	−	0.424104i	−0.820092	+	0.572232i	$0.806078\pi$
$150$		0			0
$151$		−	1623.81i		−	0.875125i	−0.899188	−	0.437562i	$-0.855842\pi$
$151$		−	1623.81i		−	0.875125i	0.899188	−	0.437562i	$-0.144158\pi$
$152$	−243.114	+	421.086i	−0.129731	+	0.224701i
$153$		0			0
$154$	848.748	−	490.025i	0.444117	−	0.256411i
$155$	664.346			0.344268
$156$		0			0
$157$	−2795.18			−1.42089			−0.710445	−	0.703753i	$-0.751506\pi$
$157$	−2795.18			−1.42089			−0.710445	+	0.703753i	$0.751506\pi$
$158$	−1058.43	+	611.085i	−0.532938	+	0.307692i
$159$		0			0
$160$	52.9006	−	91.6265i	0.0261385	−	0.0452732i
$161$			3902.08i			1.91010i
$162$		0			0
$163$	250.884	+	144.848i	0.120557	+	0.0696036i	0.559066	−	0.829123i	$-0.311160\pi$
$163$	250.884	+	144.848i	0.120557	+	0.0696036i	−0.438509	+	0.898727i	$0.644493\pi$
$164$		−	884.321i		−	0.421060i
$165$		0			0
$166$	491.565	+	851.415i	0.229836	+	0.398088i
$167$	−2016.21	+	1164.06i	−0.934246	+	0.539387i	−0.888152	−	0.459550i	$-0.848011\pi$
$167$	−2016.21	+	1164.06i	−0.934246	+	0.539387i	−0.0460940	+	0.998937i	$0.514677\pi$
$168$		0			0
$169$	1898.08	+	1106.40i	0.863940	+	0.503595i
$170$	712.357			0.321384
$171$		0			0
$172$	−224.136	−	388.214i	−0.0993615	−	0.172099i
$173$	−531.941	+	921.349i	−0.233773	+	0.404907i	−0.958915	−	0.283692i	$-0.908441\pi$
$173$	−531.941	+	921.349i	−0.233773	+	0.404907i	0.725142	+	0.688599i	$0.241774\pi$
$174$		0			0
$175$	3100.94	+	1790.33i	1.33948	+	0.773349i
$176$	216.308	+	124.885i	0.0926409	+	0.0534863i
$177$		0			0
$178$	377.155	−	653.252i	0.158814	−	0.275075i
$179$	−1235.50	−	2139.95i	−0.515898	−	0.893561i	−0.999830	−	0.0184553i	$-0.994125\pi$
$179$	−1235.50	−	2139.95i	−0.515898	−	0.893561i	0.483932	−	0.875106i	$-0.339208\pi$
$180$		0			0
$181$	−2196.50			−0.902014			−0.451007	−	0.892520i	$-0.648935\pi$
$181$	−2196.50			−0.902014			−0.451007	+	0.892520i	$0.648935\pi$
$182$	2840.81	+	767.524i	1.15701	+	0.312597i
$183$		0			0
$184$	−861.231	+	497.232i	−0.345059	+	0.199220i
$185$	173.603	+	300.689i	0.0689921	+	0.119498i
$186$		0			0
$187$			1681.70i			0.657637i
$188$	1773.97	+	1024.20i	0.688193	+	0.397329i
$189$		0			0
$190$			401.903i			0.153458i
$191$	1025.60	−	1776.39i	0.388534	−	0.672960i	−0.603719	−	0.797197i	$-0.706315\pi$
$191$	1025.60	−	1776.39i	0.388534	−	0.672960i	0.992253	+	0.124237i	$0.0396483\pi$
$192$		0			0
$193$	3250.32	−	1876.57i	1.21224	−	0.699889i	0.248996	−	0.968505i	$-0.419899\pi$
$193$	3250.32	−	1876.57i	1.21224	−	0.699889i	0.963247	+	0.268616i	$0.0865661\pi$
$194$	1146.62			0.424344
$195$		0			0
$196$	2569.43			0.936380
$197$	646.501	−	373.258i	0.233814	−	0.134992i	−0.378516	−	0.925595i	$-0.623566\pi$
$197$	646.501	−	373.258i	0.233814	−	0.134992i	0.612330	+	0.790602i	$0.290232\pi$
$198$		0			0
$199$	−1328.65	+	2301.28i	−0.473293	+	0.819767i	−0.999533	−	0.0305691i	$-0.990268\pi$
$199$	−1328.65	+	2301.28i	−0.473293	+	0.819767i	0.526240	+	0.850336i	$0.323601\pi$
$200$			912.548i			0.322634i
$201$		0			0
$202$	1654.98	+	955.502i	0.576455	+	0.332816i
$203$			1826.93i			0.631651i
$204$		0			0
$205$	−365.477	−	633.026i	−0.124517	−	0.215670i
$206$	2561.63	−	1478.96i	0.866394	−	0.500213i
$207$		0			0
$208$	192.597	+	724.802i	0.0642028	+	0.241615i
$209$	−948.794			−0.314016
$210$		0			0
$211$	753.671	+	1305.40i	0.245900	+	0.425911i	0.962384	−	0.271692i	$-0.0875832\pi$
$211$	753.671	+	1305.40i	0.245900	+	0.425911i	−0.716484	+	0.697603i	$0.754250\pi$
$212$	443.510	−	768.181i	0.143681	−	0.248863i
$213$		0			0
$214$	−369.127	−	213.116i	−0.117911	−	0.0680761i
$215$	−320.887	−	185.264i	−0.101787	−	0.0587670i
$216$		0			0
$217$	−3153.70	+	5462.37i	−0.986576	+	1.70880i
$218$	−84.4197	−	146.219i	−0.0262276	−	0.0454276i
$219$		0			0
$220$	206.453			0.0632686
$221$	−3577.90	+	3563.06i	−1.08903	+	1.08451i
$222$		0			0
$223$	1713.91	−	989.529i	0.514673	−	0.297147i	−0.220079	−	0.975482i	$-0.570632\pi$
$223$	1713.91	−	989.529i	0.514673	−	0.297147i	0.734753	+	0.678335i	$0.237298\pi$
$224$	502.246	+	869.916i	0.149811	+	0.259481i
$225$		0			0
$226$		−	1572.84i		−	0.462936i
$227$	1828.00	+	1055.39i	0.534486	+	0.308586i	0.742841	−	0.669467i	$-0.233478\pi$
$227$	1828.00	+	1055.39i	0.534486	+	0.308586i	−0.208355	+	0.978053i	$0.566811\pi$
$228$		0			0
$229$		−	5326.76i		−	1.53713i	−0.639774	−	0.768563i	$-0.720972\pi$
$229$		−	5326.76i		−	1.53713i	0.639774	−	0.768563i	$-0.279028\pi$
$230$	−410.998	+	711.870i	−0.117828	+	0.204084i
$231$		0			0
$232$	−403.223	+	232.801i	−0.114107	+	0.0658798i
$233$	−148.949			−0.0418797			−0.0209398	−	0.999781i	$-0.506666\pi$
$233$	−148.949			−0.0418797			−0.0209398	+	0.999781i	$0.506666\pi$
$234$		0			0
$235$	1693.16			0.469997
$236$	1929.24	−	1113.85i	0.532131	−	0.307226i
$237$		0			0
$238$	−3381.61	+	5857.13i	−0.920998	+	1.59522i
$239$		−	3081.18i		−	0.833912i	−0.908927	−	0.416956i	$-0.863097\pi$
$239$		−	3081.18i		−	0.833912i	0.908927	−	0.416956i	$-0.136903\pi$
$240$		0			0
$241$	2225.94	+	1285.15i	0.594960	+	0.343500i	0.767056	−	0.641580i	$-0.221721\pi$
$241$	2225.94	+	1285.15i	0.594960	+	0.343500i	−0.172096	+	0.985080i	$0.555054\pi$
$242$		−	2174.61i		−	0.577643i
$243$		0			0
$244$	−916.418	−	1587.28i	−0.240441	−	0.416456i
$245$	1839.28	−	1061.91i	0.479621	−	0.276909i
$246$		0			0
$247$	−2010.23	−	2018.60i	−0.517846	−	0.520003i
$248$	−1607.47			−0.411591
$249$		0			0
$250$	790.429	+	1369.06i	0.199965	+	0.346349i
$251$	1021.88	−	1769.95i	0.256974	−	0.445093i	−0.708456	−	0.705755i	$-0.750608\pi$
$251$	1021.88	−	1769.95i	0.256974	−	0.445093i	0.965430	+	0.260663i	$0.0839411\pi$
$252$		0			0
$253$	−1680.55	−	970.265i	−0.417609	−	0.241107i
$254$	1268.65	+	732.455i	0.313394	+	0.180938i
$255$		0			0
$256$	−128.000	+	221.703i	−0.0312500	+	0.0541266i
$257$	−3859.47	−	6684.79i	−0.936758	−	1.62251i	−0.771468	−	0.636268i	$-0.780477\pi$
$257$	−3859.47	−	6684.79i	−0.936758	−	1.62251i	−0.165290	−	0.986245i	$-0.552856\pi$
$258$		0			0
$259$	−3296.43			−0.790849
$260$	437.418	+	439.239i	0.104336	+	0.104771i
$261$		0			0
$262$	3225.78	−	1862.41i	0.760647	−	0.439160i
$263$	742.261	+	1285.63i	0.174030	+	0.301428i	0.939825	−	0.341656i	$-0.110988\pi$
$263$	742.261	+	1285.63i	0.174030	+	0.301428i	−0.765795	+	0.643084i	$0.777655\pi$
$264$		0			0
$265$		−	733.185i		−	0.169959i
$266$	−3304.52	−	1907.86i	−0.761702	−	0.439769i
$267$		0			0
$268$		−	2118.96i		−	0.482971i
$269$	−1133.27	+	1962.88i	−0.256865	+	0.444904i	−0.965400	−	0.260772i	$-0.916023\pi$
$269$	−1133.27	+	1962.88i	−0.256865	+	0.444904i	0.708535	+	0.705675i	$0.249356\pi$
$270$		0			0
$271$	4561.73	−	2633.72i	1.02253	−	0.590357i	0.107693	−	0.994184i	$-0.465654\pi$
$271$	4561.73	−	2633.72i	1.02253	−	0.590357i	0.914835	+	0.403827i	$0.132320\pi$
$272$	−1723.64			−0.384232
$273$		0			0
$274$	−1774.91			−0.391337
$275$	−1542.12	+	890.342i	−0.338157	+	0.195235i
$276$		0			0
$277$	−2407.72	+	4170.29i	−0.522260	+	0.904580i	0.477405	+	0.878683i	$0.341577\pi$
$277$	−2407.72	+	4170.29i	−0.522260	+	0.904580i	−0.999665	+	0.0258968i	$0.991756\pi$
$278$			2904.24i			0.626564i
$279$		0			0
$280$	719.048	+	415.143i	0.153469	+	0.0886054i
$281$			1983.72i			0.421134i	0.977579	+	0.210567i	$0.0675310\pi$
$281$			1983.72i			0.421134i	−0.977579	+	0.210567i	$0.932469\pi$
$282$		0			0
$283$	−413.551	−	716.291i	−0.0868658	−	0.150456i	0.819319	−	0.573338i	$-0.194352\pi$
$283$	−413.551	−	716.291i	−0.0868658	−	0.150456i	−0.906185	+	0.422882i	$0.861018\pi$
$284$	−234.003	+	135.102i	−0.0488927	+	0.0282282i
$285$		0			0
$286$	−1036.94	+	1032.64i	−0.214389	+	0.213500i
$287$	6939.80			1.42733
$288$		0			0
$289$	−3346.13	−	5795.66i	−0.681076	−	1.17966i
$290$	−192.427	+	333.292i	−0.0389644	+	0.0674883i
$291$		0			0
$292$	362.013	+	209.008i	0.0725521	+	0.0418880i
$293$	1027.62	+	593.298i	0.204895	+	0.118296i	0.598937	−	0.800796i	$-0.295590\pi$
$293$	1027.62	+	593.298i	0.204895	+	0.118296i	−0.394041	+	0.919093i	$0.628923\pi$
$294$		0			0
$295$	920.676	−	1594.66i	0.181708	−	0.314727i
$296$	−420.055	−	727.557i	−0.0824839	−	0.142866i
$297$		0			0
$298$	3085.40			0.599774
$299$	−1496.33	−	5631.17i	−0.289415	−	1.08916i
$300$		0			0
$301$	3046.55	−	1758.93i	0.583389	−	0.336820i
$302$	1623.81	+	2812.52i	0.309403	+	0.535902i
$303$		0			0
$304$		−	972.457i		−	0.183468i
$305$	−1312.00	−	757.485i	−0.246312	−	0.142208i
$306$		0			0
$307$			6191.17i			1.15097i	0.817811	+	0.575486i	$0.195187\pi$
$307$			6191.17i			1.15097i	−0.817811	+	0.575486i	$0.804813\pi$
$308$	−980.050	+	1697.50i	−0.181310	+	0.314038i
$309$		0			0
$310$	−1150.68	+	664.346i	−0.210820	+	0.121717i
$311$	−10609.3			−1.93440			−0.967198	−	0.254024i	$-0.918246\pi$
$311$	−10609.3			−1.93440			−0.967198	+	0.254024i	$0.918246\pi$
$312$		0			0
$313$	9833.23			1.77574			0.887871	−	0.460093i	$-0.152184\pi$
$313$	9833.23			1.77574			0.887871	+	0.460093i	$0.152184\pi$
$314$	4841.39	−	2795.18i	0.870114	−	0.502360i
$315$		0			0
$316$	1222.17	−	2116.86i	0.217571	−	0.376844i
$317$			4674.74i			0.828263i	0.910217	+	0.414131i	$0.135915\pi$
$317$			4674.74i			0.828263i	−0.910217	+	0.414131i	$0.864085\pi$
$318$		0			0
$319$	−786.822	−	454.272i	−0.138099	−	0.0797314i
$320$			211.602i			0.0369654i
$321$		0			0
$322$	−3902.08	−	6758.60i	−0.675324	−	1.16970i
$323$	5670.33	−	3273.77i	0.976798	−	0.563954i
$324$		0			0
$325$	−5161.57	−	1394.54i	−0.880961	−	0.238016i
$326$	−579.393			−0.0984344
$327$		0			0
$328$	884.321	+	1531.69i	0.148867	+	0.257846i
$329$	−8037.54	+	13921.4i	−1.34688	+	2.33287i
$330$		0			0
$331$	−9018.24	−	5206.68i	−1.49755	−	0.864608i	−0.497549	−	0.867436i	$-0.665767\pi$
$331$	−9018.24	−	5206.68i	−1.49755	−	0.864608i	−0.999996	+	0.00282772i	$0.999100\pi$
$332$	−1702.83	−	983.130i	−0.281491	−	0.162519i
$333$		0			0
$334$	2328.12	−	4032.42i	0.381404	−	0.660612i
$335$	−875.737	−	1516.82i	−0.142826	−	0.247381i
$336$		0			0
$337$	−4873.47			−0.787759			−0.393879	−	0.919162i	$-0.628867\pi$
$337$	−4873.47			−0.787759			−0.393879	+	0.919162i	$0.628867\pi$
$338$	−4393.96	−	18.2620i	−0.707101	−	0.00293882i
$339$		0			0
$340$	−1233.84	+	712.357i	−0.196807	+	0.113626i
$341$	−1568.36	−	2716.47i	−0.249065	−	0.431394i
$342$		0			0
$343$			9396.92i			1.47926i
$344$	776.428	+	448.271i	0.121692	+	0.0702592i
$345$		0			0
$346$		−	2127.77i		−	0.330605i
$347$	6060.84	−	10497.7i	0.937645	−	1.62405i	0.167798	−	0.985821i	$-0.446334\pi$
$347$	6060.84	−	10497.7i	0.937645	−	1.62405i	0.769847	−	0.638228i	$-0.220332\pi$
$348$		0			0
$349$	−7683.52	+	4436.08i	−1.17848	+	0.680396i	−0.955663	−	0.294464i	$-0.904859\pi$
$349$	−7683.52	+	4436.08i	−1.17848	+	0.680396i	−0.222818	+	0.974860i	$0.571526\pi$
$350$	−7161.31			−1.09368
$351$		0			0
$352$	−499.541			−0.0756410
$353$	3933.22	−	2270.84i	0.593043	−	0.342393i	−0.173257	−	0.984877i	$-0.555429\pi$
$353$	3933.22	−	2270.84i	0.593043	−	0.342393i	0.766300	+	0.642483i	$0.222096\pi$
$354$		0			0
$355$	−111.671	+	193.420i	−0.0166955	+	0.0289174i
$356$			1508.62i			0.224598i
$357$		0			0
$358$	4279.90	+	2471.00i	0.631843	+	0.364795i
$359$			1398.34i			0.205576i	0.994703	+	0.102788i	$0.0327763\pi$
$359$			1398.34i			0.205576i	−0.994703	+	0.102788i	$0.967224\pi$
$360$		0			0
$361$	−1582.48	−	2740.94i	−0.230716	−	0.399612i
$362$	3804.45	−	2196.50i	0.552368	−	0.318910i
$363$		0			0
$364$	−5687.96	+	1511.42i	−0.819038	+	0.217637i
$365$	345.521			0.0495490
$366$		0			0
$367$	−2019.26	−	3497.46i	−0.287205	−	0.497454i	0.685936	−	0.727662i	$-0.259393\pi$
$367$	−2019.26	−	3497.46i	−0.287205	−	0.497454i	−0.973142	+	0.230207i	$0.926060\pi$
$368$	994.464	−	1722.46i	0.140870	−	0.243993i
$369$		0			0
$370$	−601.378	−	347.206i	−0.0844978	−	0.0487848i
$371$	6028.38	+	3480.49i	0.843606	+	0.487056i
$372$		0			0
$373$	−315.134	+	545.828i	−0.0437454	+	0.0757692i	−0.887069	−	0.461637i	$-0.847262\pi$
$373$	−315.134	+	545.828i	−0.0437454	+	0.0757692i	0.843324	+	0.537406i	$0.180596\pi$
$374$	−1681.70	−	2912.79i	−0.232510	−	0.402719i
$375$		0			0
$376$	−4096.82			−0.561908
$377$	−700.573	−	2636.48i	−0.0957065	−	0.360174i
$378$		0			0
$379$	4259.91	−	2459.46i	0.577353	−	0.333335i	−0.182728	−	0.983164i	$-0.558493\pi$
$379$	4259.91	−	2459.46i	0.577353	−	0.333335i	0.760081	+	0.649828i	$0.225159\pi$
$380$	−401.903	−	696.116i	−0.0542557	−	0.0939737i
$381$		0			0
$382$			4102.41i			0.549470i
$383$	8681.96	+	5012.53i	1.15830	+	0.668742i	0.950895	−	0.309514i	$-0.100166\pi$
$383$	8681.96	+	5012.53i	1.15830	+	0.668742i	0.207401	+	0.978256i	$0.433500\pi$
$384$		0			0
$385$			1620.16i			0.214471i
$386$	−3753.14	+	6500.63i	−0.494896	+	0.857185i
$387$		0			0
$388$	−1986.01	+	1146.62i	−0.259857	+	0.150028i
$389$	13329.5			1.73735			0.868676	−	0.495380i	$-0.164971\pi$
$389$	13329.5			1.73735			0.868676	+	0.495380i	$0.164971\pi$
$390$		0			0
$391$	13391.4			1.73205
$392$	−4450.38	+	2569.43i	−0.573413	+	0.331060i
$393$		0			0
$394$	−746.515	+	1293.00i	−0.0954540	+	0.165331i
$395$		−	2020.42i		−	0.257363i
$396$		0			0
$397$	401.196	+	231.631i	0.0507191	+	0.0292827i	0.525145	−	0.851013i	$-0.324011\pi$
$397$	401.196	+	231.631i	0.0507191	+	0.0292827i	−0.474426	+	0.880295i	$0.657344\pi$
$398$		−	5314.59i		−	0.669337i
$399$		0			0
$400$	−912.548	−	1580.58i	−0.114068	−	0.197572i
$401$	−12170.0	+	7026.32i	−1.51556	+	0.875007i	−0.515723	+	0.856755i	$0.672477\pi$
$401$	−12170.0	+	7026.32i	−1.51556	+	0.875007i	−0.999833	+	0.0182521i	$0.994190\pi$
$402$		0			0
$403$	2456.51	−	9092.21i	0.303642	−	1.12386i
$404$	−3822.01			−0.470673
$405$		0			0
$406$	−1826.93	−	3164.33i	−0.223322	−	0.386805i
$407$	819.668	−	1419.71i	0.0998266	−	0.172905i
$408$		0			0
$409$	−3844.75	−	2219.77i	−0.464819	−	0.268363i	0.249250	−	0.968439i	$-0.419816\pi$
$409$	−3844.75	−	2219.77i	−0.464819	−	0.268363i	−0.714068	+	0.700076i	$0.753149\pi$
$410$	1266.05	+	730.955i	0.152502	+	0.0880471i
$411$		0			0
$412$	−2957.91	+	5123.26i	−0.353704	+	0.612633i
$413$	8741.03	+	15139.9i	1.04145	+	1.80384i
$414$		0			0
$415$	−1625.25			−0.192242
$416$	−1058.39	−	1062.80i	−0.124740	−	0.125259i
$417$		0			0
$418$	1643.36	−	948.794i	0.192295	−	0.111022i
$419$	−6839.51	−	11846.4i	−0.797451	−	1.38123i	−0.921271	−	0.388921i	$-0.872848\pi$
$419$	−6839.51	−	11846.4i	−0.797451	−	1.38123i	0.123820	−	0.992305i	$-0.460486\pi$
$420$		0			0
$421$			11133.2i			1.28884i	0.764673	+	0.644419i	$0.222901\pi$
$421$			11133.2i			1.28884i	−0.764673	+	0.644419i	$0.777099\pi$
$422$	−2610.79	−	1507.34i	−0.301165	−	0.173877i
$423$		0			0
$424$			1774.04i			0.203196i
$425$	6144.17	−	10642.0i	0.701261	−	1.21462i
$426$		0			0
$427$	12456.4	−	7191.68i	1.41172	−	0.815058i
$428$	852.463			0.0962741
$429$		0			0
$430$	741.057			0.0831091
$431$	1259.28	−	727.043i	0.140736	−	0.0812539i	−0.427979	−	0.903789i	$-0.640774\pi$
$431$	1259.28	−	727.043i	0.140736	−	0.0812539i	0.568715	+	0.822535i	$0.307441\pi$
$432$		0			0
$433$	−3844.28	+	6658.49i	−0.426662	+	0.738999i	−0.996574	−	0.0827060i	$-0.973644\pi$
$433$	−3844.28	+	6658.49i	−0.426662	+	0.738999i	0.569912	+	0.821705i	$0.306977\pi$
$434$		−	12614.8i		−	1.39523i
$435$		0			0
$436$	292.438	+	168.839i	0.0321222	+	0.0185457i
$437$			7555.26i			0.827042i
$438$		0			0
$439$	−4320.81	−	7483.86i	−0.469751	−	0.813633i	0.529651	−	0.848216i	$-0.322323\pi$
$439$	−4320.81	−	7483.86i	−0.469751	−	0.813633i	−0.999402	+	0.0345828i	$0.988990\pi$
$440$	−357.588	+	206.453i	−0.0387439	+	0.0223688i
$441$		0			0
$442$	2634.04	−	9749.30i	0.283458	−	1.04916i
$443$	13563.6			1.45469			0.727346	−	0.686271i	$-0.240754\pi$
$443$	13563.6			1.45469			0.727346	+	0.686271i	$0.240754\pi$
$444$		0			0
$445$	623.492	+	1079.92i	0.0664187	+	0.115041i
$446$	−1979.06	+	3427.83i	−0.210115	+	0.363929i
$447$		0			0
$448$	−1739.83	−	1004.49i	−0.183481	−	0.105933i
$449$	−16278.9	−	9398.65i	−1.71103	−	0.987862i	−0.933181	−	0.359406i	$-0.882979\pi$
$449$	−16278.9	−	9398.65i	−1.71103	−	0.987862i	−0.777845	−	0.628456i	$-0.783687\pi$
$450$		0			0
$451$	−1725.60	+	2988.84i	−0.180168	+	0.312059i
$452$	1572.84	+	2724.23i	0.163673	+	0.283489i
$453$		0			0
$454$	−4221.58			−0.436406
$455$	−3446.97	+	3432.68i	−0.355157	+	0.353684i
$456$		0			0
$457$	6257.55	−	3612.80i	0.640516	−	0.369802i	−0.144297	−	0.989534i	$-0.546092\pi$
$457$	6257.55	−	3612.80i	0.640516	−	0.369802i	0.784813	+	0.619732i	$0.212759\pi$
$458$	5326.76	+	9226.21i	0.543456	+	0.941294i
$459$		0			0
$460$		−	1643.99i		−	0.166634i
$461$	−1987.84	−	1147.68i	−0.200831	−	0.115950i	0.396212	−	0.918159i	$-0.370324\pi$
$461$	−1987.84	−	1147.68i	−0.200831	−	0.115950i	−0.597043	+	0.802209i	$0.703658\pi$
$462$		0			0
$463$			9457.75i			0.949328i	0.880167	+	0.474664i	$0.157430\pi$
$463$			9457.75i			0.949328i	−0.880167	+	0.474664i	$0.842570\pi$
$464$	465.601	−	806.445i	0.0465841	−	0.0806859i
$465$		0			0
$466$	257.987	−	148.949i	0.0256460	−	0.0148067i
$467$	−13310.9			−1.31896			−0.659481	−	0.751721i	$-0.729224\pi$
$467$	−13310.9			−1.31896			−0.659481	+	0.751721i	$0.729224\pi$
$468$		0			0
$469$	16628.8			1.63720
$470$	−2932.63	+	1693.16i	−0.287813	+	0.166169i
$471$		0			0
$472$	−2227.70	+	3858.48i	−0.217242	+	0.376273i
$473$			1749.45i			0.170063i
$474$		0			0
$475$	6004.08	+	3466.46i	0.579971	+	0.334846i
$476$		−	13526.5i		−	1.30249i
$477$		0			0
$478$	3081.18	+	5336.76i	0.294833	+	0.510665i
$479$	6901.57	−	3984.62i	0.658332	−	0.380088i	−0.133309	−	0.991074i	$-0.542560\pi$
$479$	6901.57	−	3984.62i	0.658332	−	0.380088i	0.791641	+	0.610987i	$0.209227\pi$
$480$		0			0
$481$	4757.14	−	1264.08i	0.450950	−	0.119828i
$482$	−5140.59			−0.485783
$483$		0			0
$484$	2174.61	+	3766.54i	0.204228	+	0.353732i
$485$	−947.767	+	1641.58i	−0.0887338	+	0.153691i
$486$		0			0
$487$	−1225.83	−	707.734i	−0.114061	−	0.0658532i	0.441884	−	0.897072i	$-0.354310\pi$
$487$	−1225.83	−	707.734i	−0.114061	−	0.0658532i	−0.555945	+	0.831219i	$0.687644\pi$
$488$	3174.57	+	1832.84i	0.294479	+	0.170018i
$489$		0			0
$490$	−2123.82	+	3678.56i	−0.195805	+	0.339143i
$491$	1600.46	+	2772.07i	0.147103	+	0.254790i	0.930156	−	0.367166i	$-0.119672\pi$
$491$	1600.46	+	2772.07i	0.147103	+	0.254790i	−0.783053	+	0.621956i	$0.786338\pi$
$492$		0			0
$493$	6269.77			0.572771
$494$	5500.43	+	1486.09i	0.500963	+	0.135349i
$495$		0			0
$496$	2784.22	−	1607.47i	0.252047	−	0.145519i
$497$	−1060.22	−	1836.36i	−0.0956892	−	0.165739i
$498$		0			0
$499$		−	1480.51i		−	0.132819i	−0.997792	−	0.0664097i	$-0.978846\pi$
$499$		−	1480.51i		−	0.132819i	0.997792	−	0.0664097i	$-0.0211544\pi$
$500$	−2738.13	−	1580.86i	−0.244905	−	0.141396i
$501$		0			0
$502$			4087.52i			0.363417i
$503$	−10129.6	+	17545.1i	−0.897929	+	1.55526i	−0.0677919	+	0.997699i	$0.521595\pi$
$503$	−10129.6	+	17545.1i	−0.897929	+	1.55526i	−0.830137	+	0.557559i	$0.811738\pi$
$504$		0			0
$505$	−2735.92	+	1579.58i	−0.241083	+	0.139189i
$506$	3881.06			0.340977
$507$		0			0
$508$	−2929.82			−0.255885
$509$	6122.14	−	3534.62i	0.533122	−	0.307798i	−0.209165	−	0.977880i	$-0.567075\pi$
$509$	6122.14	−	3534.62i	0.533122	−	0.307798i	0.742287	+	0.670082i	$0.233741\pi$
$510$		0			0
$511$	−1640.21	+	2840.93i	−0.141994	+	0.245940i
$512$		−	512.000i		−	0.0441942i
$513$		0			0
$514$	13369.6	+	7718.93i	1.14729	+	0.662388i
$515$			4889.86i			0.418394i
$516$		0			0
$517$	−3997.13	−	6923.23i	−0.340026	−	0.588942i
$518$	5709.58	−	3296.43i	0.484294	−	0.279607i
$519$		0			0
$520$	−1196.87	−	323.367i	−0.100935	−	0.0272704i
$521$	13874.4			1.16670			0.583348	−	0.812223i	$-0.301743\pi$
$521$	13874.4			1.16670			0.583348	+	0.812223i	$0.301743\pi$
$522$		0			0
$523$	8176.89	+	14162.8i	0.683653	+	1.18412i	0.973858	+	0.227158i	$0.0729432\pi$
$523$	8176.89	+	14162.8i	0.683653	+	1.18412i	−0.290205	+	0.956965i	$0.593723\pi$
$524$	−3724.82	+	6451.57i	−0.310533	+	0.537859i
$525$		0			0
$526$	−2571.27	−	1484.52i	−0.213142	−	0.123057i
$527$	18746.1	+	10823.1i	1.54951	+	0.894613i
$528$		0			0
$529$	−1642.74	+	2845.31i	−0.135016	+	0.233855i
$530$	733.185	+	1269.91i	0.0600897	+	0.104078i
$531$		0			0
$532$	7631.45			0.621927
$533$	−10015.0	+	2661.21i	−0.813877	+	0.216266i
$534$		0			0
$535$	610.220	−	352.311i	0.0493124	−	0.0284705i
$536$	2118.96	+	3670.15i	0.170756	+	0.295758i
$537$		0			0
$538$		−	4533.08i		−	0.363262i
$539$	−8684.17	−	5013.81i	−0.693977	−	0.400668i
$540$		0			0
$541$		−	2609.54i		−	0.207381i	−0.994610	−	0.103690i	$-0.966935\pi$
$541$		−	2609.54i		−	0.207381i	0.994610	−	0.103690i	$-0.0330651\pi$
$542$	−5267.43	+	9123.46i	−0.417446	+	0.723037i
$543$		0			0
$544$	2985.44	−	1723.64i	0.235293	−	0.135847i
$545$	279.116			0.0219376
$546$		0			0
$547$	−22168.6			−1.73284			−0.866419	−	0.499318i	$-0.833584\pi$
$547$	−22168.6			−1.73284			−0.866419	+	0.499318i	$0.833584\pi$
$548$	3074.24	−	1774.91i	0.239644	−	0.138358i
$549$		0			0
$550$	1780.68	−	3084.24i	0.138052	−	0.239113i
$551$			3537.32i			0.273494i
$552$		0			0
$553$	16612.3	+	9591.09i	1.27744	+	0.737531i
$554$		−	9630.88i		−	0.738587i
$555$		0			0
$556$	−2904.24	−	5030.29i	−0.221524	−	0.383690i
$557$	18090.3	−	10444.4i	1.37614	−	0.794514i	0.384446	−	0.923147i	$-0.374392\pi$
$557$	18090.3	−	10444.4i	1.37614	−	0.794514i	0.991692	+	0.128634i	$0.0410591\pi$
$558$		0			0
$559$	−3722.04	+	3706.61i	−0.281620	+	0.280452i
$560$	−1660.57			−0.125307
$561$		0			0
$562$	−1983.72	−	3435.90i	−0.148893	−	0.257891i
$563$	−6340.33	+	10981.8i	−0.474623	+	0.822071i	−0.999578	−	0.0290588i	$-0.990749\pi$
$563$	−6340.33	+	10981.8i	−0.474623	+	0.822071i	0.524955	+	0.851130i	$0.324082\pi$
$564$		0			0
$565$	2251.77	+	1300.06i	0.167669	+	0.0968036i
$566$	1432.58	+	827.101i	0.106388	+	0.0614234i
$567$		0			0
$568$	270.203	−	468.006i	0.0199604	−	0.0345723i
$569$	316.343	+	547.922i	0.0233072	+	0.0403692i	0.877444	−	0.479680i	$-0.159247\pi$
$569$	316.343	+	547.922i	0.0233072	+	0.0403692i	−0.854137	+	0.520049i	$0.825914\pi$
$570$		0			0
$571$	−8050.66			−0.590034			−0.295017	−	0.955492i	$-0.595325\pi$
$571$	−8050.66			−0.590034			−0.295017	+	0.955492i	$0.595325\pi$
$572$	763.391	−	2825.51i	0.0558024	−	0.206540i
$573$		0			0
$574$	−12020.1	+	6939.80i	−0.874057	+	0.504637i
$575$	7089.81	+	12279.9i	0.514201	+	0.890622i
$576$		0			0
$577$			14173.9i			1.02265i	0.859389	+	0.511323i	$0.170844\pi$
$577$			14173.9i			1.02265i	−0.859389	+	0.511323i	$0.829156\pi$
$578$	11591.3	+	6692.26i	0.834145	+	0.481594i
$579$		0			0
$580$		−	769.706i		−	0.0551040i
$581$	7715.21	−	13363.1i	0.550913	−	0.954210i
$582$		0			0
$583$	−2997.96	+	1730.87i	−0.212972	+	0.122959i
$584$	−836.033			−0.0592385
$585$		0			0
$586$	−2373.19			−0.167296
$587$	−11411.7	+	6588.56i	−0.802406	+	0.463269i	−0.844312	−	0.535852i	$-0.819990\pi$
$587$	−11411.7	+	6588.56i	−0.802406	+	0.463269i	0.0419057	+	0.999122i	$0.486657\pi$
$588$		0			0
$589$	−6106.24	+	10576.3i	−0.427170	+	0.739881i
$590$			3682.70i			0.256974i
$591$		0			0
$592$	1455.11	+	840.111i	0.101022	+	0.0583249i
$593$		−	20637.4i		−	1.42913i	−0.699568	−	0.714566i	$-0.746624\pi$
$593$		−	20637.4i		−	1.42913i	0.699568	−	0.714566i	$-0.253376\pi$
$594$		0			0
$595$	−5590.30	−	9682.68i	−0.385176	−	0.667145i
$596$	−5344.08	+	3085.40i	−0.367285	+	0.212052i
$597$		0			0
$598$	8222.90	+	8257.14i	0.562306	+	0.564648i
$599$	−286.244			−0.0195252			−0.00976262	−	0.999952i	$-0.503108\pi$
$599$	−286.244			−0.0195252			−0.00976262	+	0.999952i	$0.503108\pi$
$600$		0			0
$601$	−10160.8	−	17599.1i	−0.689633	−	1.19448i	−0.971957	−	0.235160i	$-0.924439\pi$
$601$	−10160.8	−	17599.1i	−0.689633	−	1.19448i	0.282324	−	0.959319i	$-0.408895\pi$
$602$	−3517.85	+	6093.10i	−0.238168	+	0.412518i
$603$		0			0
$604$	−5625.04	−	3247.62i	−0.378940	−	0.218781i
$605$	3113.32	+	1797.48i	0.209214	+	0.120790i
$606$		0			0
$607$	−2454.43	+	4251.19i	−0.164122	+	0.284268i	−0.936343	−	0.351086i	$-0.885812\pi$
$607$	−2454.43	+	4251.19i	−0.164122	+	0.284268i	0.772221	+	0.635354i	$0.219146\pi$
$608$	972.457	+	1684.35i	0.0648657	+	0.112351i
$609$		0			0
$610$	3029.94			0.201113
$611$	6260.69	−	23172.5i	0.414534	−	1.53430i
$612$		0			0
$613$	−7008.38	+	4046.29i	−0.461771	+	0.266604i	−0.712789	−	0.701379i	$-0.752568\pi$
$613$	−7008.38	+	4046.29i	−0.461771	+	0.266604i	0.251018	+	0.967983i	$0.419235\pi$
$614$	−6191.17	−	10723.4i	−0.406930	−	0.704824i
$615$		0			0
$616$		−	3920.20i		−	0.256411i
$617$	−19404.8	−	11203.4i	−1.26614	−	0.731006i	−0.291884	−	0.956454i	$-0.594282\pi$
$617$	−19404.8	−	11203.4i	−1.26614	−	0.731006i	−0.974255	+	0.225448i	$0.927615\pi$
$618$		0			0
$619$		−	29226.6i		−	1.89777i	−0.315627	−	0.948883i	$-0.602215\pi$
$619$		−	29226.6i		−	1.89777i	0.315627	−	0.948883i	$-0.397785\pi$
$620$	1328.69	−	2301.36i	0.0860670	−	0.149072i
$621$		0			0
$622$	18375.8	−	10609.3i	1.18457	−	0.683912i
$623$	−11839.0			−0.761351
$624$		0			0
$625$	11645.2			0.745291
$626$	−17031.7	+	9833.23i	−1.08742	+	0.627819i
$627$		0			0
$628$	−5590.36	+	9682.79i	−0.355222	+	0.615263i
$629$			11312.9i			0.717130i
$630$		0			0
$631$	5473.32	+	3160.03i	0.345308	+	0.199364i	0.662617	−	0.748958i	$-0.269446\pi$
$631$	5473.32	+	3160.03i	0.345308	+	0.199364i	−0.317309	+	0.948322i	$0.602779\pi$
$632$			4888.68i			0.307692i
$633$		0			0
$634$	−4674.74	−	8096.88i	−0.292835	−	0.507205i
$635$	−2097.26	+	1210.85i	−0.131066	+	0.0756712i
$636$		0			0
$637$	−7732.24	−	29098.9i	−0.480946	−	1.80995i
$638$	1817.09			0.112757
$639$		0			0
$640$	−211.602	−	366.506i	−0.0130692	−	0.0226366i
$641$	4201.52	−	7277.24i	0.258892	−	0.448415i	−0.707053	−	0.707160i	$-0.749976\pi$
$641$	4201.52	−	7277.24i	0.258892	−	0.448415i	0.965945	+	0.258746i	$0.0833092\pi$
$642$		0			0
$643$	−271.587	−	156.801i	−0.0166568	−	0.00961684i	0.491648	−	0.870794i	$-0.336395\pi$
$643$	−271.587	−	156.801i	−0.0166568	−	0.00961684i	−0.508305	+	0.861177i	$0.669728\pi$
$644$	13517.2	+	7804.15i	0.827099	+	0.477526i
$645$		0			0
$646$	−6547.54	+	11340.7i	−0.398776	+	0.690700i
$647$	4037.44	+	6993.04i	0.245329	+	0.424923i	0.962224	−	0.272259i	$-0.0877706\pi$
$647$	4037.44	+	6993.04i	0.245329	+	0.424923i	−0.716895	+	0.697181i	$0.754437\pi$
$648$		0			0
$649$	−8693.95			−0.525836
$650$	10334.6	−	2746.15i	0.623627	−	0.165712i
$651$		0			0
$652$	1003.54	−	579.393i	0.0602785	−	0.0348018i
$653$	−9083.36	−	15732.8i	−0.544348	−	0.942839i	−0.998648	−	0.0519898i	$-0.983444\pi$
$653$	−9083.36	−	15732.8i	−0.544348	−	0.942839i	0.454299	−	0.890849i	$-0.349890\pi$
$654$		0			0
$655$			6157.66i			0.367327i
$656$	−3063.38	−	1768.64i	−0.182324	−	0.105265i
$657$		0			0
$658$		−	32150.2i		−	1.90478i
$659$	−9822.68	+	17013.4i	−0.580633	+	1.00569i	0.414771	+	0.909926i	$0.363862\pi$
$659$	−9822.68	+	17013.4i	−0.580633	+	1.00569i	−0.995404	+	0.0957607i	$0.969472\pi$
$660$		0			0
$661$	−9515.27	+	5493.64i	−0.559911	+	0.323265i	−0.753110	−	0.657895i	$-0.771447\pi$
$661$	−9515.27	+	5493.64i	−0.559911	+	0.323265i	0.193199	+	0.981160i	$0.438114\pi$
$662$	20826.7			1.22274
$663$		0			0
$664$	3932.52			0.229836
$665$	5462.84	−	3153.97i	0.318556	−	0.183918i
$666$		0			0
$667$	−3617.37	+	6265.48i	−0.209993	+	0.363718i
$668$			9312.48i			0.539387i
$669$		0			0
$670$	3033.64	+	1751.47i	0.174925	+	0.100993i
$671$			7152.95i			0.411530i
$672$		0			0
$673$	17128.5	+	29667.5i	0.981065	+	1.69925i	0.658264	+	0.752787i	$0.271291\pi$
$673$	17128.5	+	29667.5i	0.981065	+	1.69925i	0.322801	+	0.946467i	$0.395376\pi$
$674$	8441.09	−	4873.47i	0.482402	−	0.278515i
$675$		0			0
$676$	7628.83	−	4362.33i	0.434048	−	0.248198i
$677$	−25142.1			−1.42731			−0.713656	−	0.700497i	$-0.752962\pi$
$677$	−25142.1			−1.42731			−0.713656	+	0.700497i	$0.752962\pi$
$678$		0			0
$679$	−8998.24	−	15585.4i	−0.508573	−	0.880874i
$680$	1424.71	−	2467.68i	0.0803461	−	0.139163i
$681$		0			0
$682$	5432.95	+	3136.71i	0.305041	+	0.176116i
$683$	−8664.54	−	5002.48i	−0.485416	−	0.280255i	0.237255	−	0.971448i	$-0.423752\pi$
$683$	−8664.54	−	5002.48i	−0.485416	−	0.280255i	−0.722671	+	0.691192i	$0.757086\pi$
$684$		0			0
$685$	1467.09	−	2541.08i	0.0818317	−	0.141737i
$686$	−9396.92	−	16275.9i	−0.522997	−	0.905858i
$687$		0			0
$688$	−1793.08			−0.0993615
$689$	−10034.3	−	2711.06i	−0.554831	−	0.149903i
$690$		0			0
$691$	6354.19	−	3668.59i	0.349819	−	0.201968i	−0.314787	−	0.949162i	$-0.601933\pi$
$691$	6354.19	−	3668.59i	0.349819	−	0.201968i	0.664605	+	0.747195i	$0.268600\pi$
$692$	2127.77	+	3685.40i	0.116887	+	0.202453i
$693$		0			0
$694$			24243.4i			1.32603i
$695$	−4157.90	−	2400.56i	−0.226932	−	0.131019i
$696$		0			0
$697$		−	23816.5i		−	1.29428i
$698$	8872.17	−	15367.0i	0.481113	−	0.833311i
$699$		0			0
$700$	12403.7	−	7161.31i	0.669739	−	0.386674i
$701$	−7785.35			−0.419470			−0.209735	−	0.977758i	$-0.567260\pi$
$701$	−7785.35			−0.419470			−0.209735	+	0.977758i	$0.567260\pi$
$702$		0			0
$703$	−6382.59			−0.342424
$704$	865.231	−	499.541i	0.0463205	−	0.0267431i
$705$		0			0
$706$	−4541.69	+	7866.44i	−0.242109	+	0.419345i
$707$		−	29993.6i		−	1.59551i
$708$		0			0
$709$	517.039	+	298.513i	0.0273876	+	0.0158122i	0.513631	−	0.858011i	$-0.328300\pi$
$709$	517.039	+	298.513i	0.0273876	+	0.0158122i	−0.486244	+	0.873823i	$0.661633\pi$
$710$		−	446.685i		−	0.0236110i
$711$		0			0
$712$	−1508.62	−	2613.01i	−0.0794072	−	0.137537i
$713$	−21631.3	+	12488.9i	−1.13618	+	0.655977i
$714$		0			0
$715$	−621.285	−	2338.09i	−0.0324962	−	0.122293i
$716$	−9884.01			−0.515898
$717$		0			0
$718$	−1398.34	−	2422.00i	−0.0726820	−	0.125889i
$719$	6006.81	−	10404.1i	0.311566	−	0.539648i	−0.667135	−	0.744936i	$-0.732480\pi$
$719$	6006.81	−	10404.1i	0.311566	−	0.539648i	0.978702	+	0.205288i	$0.0658131\pi$
$720$		0			0
$721$	−40205.3	−	23212.5i	−2.07673	−	1.19900i
$722$	5481.88	+	3164.97i	0.282569	+	0.163141i
$723$		0			0
$724$	−4393.00	+	7608.90i	−0.225503	+	0.390583i
$725$	3319.40	+	5749.37i	0.170041	+	0.294519i
$726$		0			0
$727$	−1137.34			−0.0580216			−0.0290108	−	0.999579i	$-0.509236\pi$
$727$	−1137.34			−0.0580216			−0.0290108	+	0.999579i	$0.509236\pi$
$728$	8340.41	−	8305.82i	0.424610	−	0.422849i
$729$		0			0
$730$	−598.460	+	345.521i	−0.0303424	+	0.0175182i
$731$	−6036.40	−	10455.4i	−0.305423	−	0.529009i
$732$		0			0
$733$		−	24930.1i		−	1.25623i	−0.778122	−	0.628113i	$-0.783828\pi$
$733$		−	24930.1i		−	1.25623i	0.778122	−	0.628113i	$-0.216172\pi$
$734$	6994.91	+	4038.51i	0.351753	+	0.203085i
$735$		0			0
$736$			3977.86i			0.199220i
$737$	−4134.80	+	7161.68i	−0.206658	+	0.357943i
$738$		0			0
$739$	−9626.47	+	5557.84i	−0.479182	+	0.276656i	−0.720075	−	0.693896i	$-0.755893\pi$
$739$	−9626.47	+	5557.84i	−0.479182	+	0.276656i	0.240894	+	0.970552i	$0.422560\pi$
$740$	1388.82			0.0689921
$741$		0			0
$742$	−13921.9			−0.688802
$743$	−10675.7	+	6163.62i	−0.527125	+	0.304336i	−0.739845	−	0.672777i	$-0.765101\pi$
$743$	−10675.7	+	6163.62i	−0.527125	+	0.304336i	0.212720	+	0.977113i	$0.431768\pi$
$744$		0			0
$745$	−2550.31	+	4417.26i	−0.125418	+	0.217230i
$746$		−	1260.54i		−	0.0618653i
$747$		0			0
$748$	5825.58	+	3363.40i	0.284765	+	0.164409i
$749$			6689.78i			0.326354i
$750$		0			0
$751$	−6902.03	−	11954.7i	−0.335364	−	0.580868i	0.648190	−	0.761478i	$-0.275526\pi$
$751$	−6902.03	−	11954.7i	−0.335364	−	0.580868i	−0.983555	+	0.180610i	$0.942193\pi$
$752$	7095.90	−	4096.82i	0.344097	−	0.198664i
$753$		0			0
$754$	3849.90	+	3865.94i	0.185949	+	0.186723i
$755$	−5368.78			−0.258795
$756$		0			0
$757$	−450.515	−	780.315i	−0.0216304	−	0.0374650i	0.855008	−	0.518616i	$-0.173552\pi$
$757$	−450.515	−	780.315i	−0.0216304	−	0.0374650i	−0.876638	+	0.481151i	$0.840219\pi$
$758$	−4918.92	+	8519.82i	−0.235704	+	0.408250i
$759$		0			0
$760$	1392.23	+	803.806i	0.0664494	+	0.0383646i
$761$	25742.3	+	14862.3i	1.22623	+	0.707962i	0.966238	−	0.257650i	$-0.0829483\pi$
$761$	25742.3	+	14862.3i	1.22623	+	0.707962i	0.259987	+	0.965612i	$0.416282\pi$
$762$		0			0
$763$	−1324.98	+	2294.94i	−0.0628671	+	0.108889i
$764$	−4102.41	−	7105.58i	−0.194267	−	0.336480i
$765$		0			0
$766$	−20050.1			−0.945745
$767$	−18420.1	−	18496.8i	−0.867159	−	0.870770i
$768$		0			0
$769$	22531.8	−	13008.7i	1.05659	−	0.610021i	0.132101	−	0.991236i	$-0.457828\pi$
$769$	22531.8	−	13008.7i	1.05659	−	0.610021i	0.924486	+	0.381215i	$0.124494\pi$
$770$	−1620.16	−	2806.20i	−0.0758268	−	0.131336i
$771$		0			0
$772$		−	15012.6i		−	0.699889i
$773$	3392.26	+	1958.52i	0.157841	+	0.0911296i	0.576840	−	0.816857i	$-0.304286\pi$
$773$	3392.26	+	1958.52i	0.157841	+	0.0911296i	−0.418999	+	0.907987i	$0.637619\pi$
$774$		0			0
$775$			22920.2i			1.06235i
$776$	2293.25	−	3972.02i	0.106086	−	0.183746i
$777$		0			0
$778$	−23087.3	+	13329.5i	−1.06391	+	0.614247i
$779$	13436.9			0.618008
$780$		0			0
$781$	1054.51			0.0483143
$782$	−23194.6	+	13391.4i	−1.06066	+	0.612374i
$783$		0			0
$784$	5138.85	−	8900.76i	0.234095	−	0.405464i
$785$			9241.67i			0.420190i
$786$		0			0
$787$	−1556.50	−	898.643i	−0.0704995	−	0.0407029i	0.464336	−	0.885659i	$-0.346293\pi$
$787$	−1556.50	−	898.643i	−0.0704995	−	0.0407029i	−0.534835	+	0.844956i	$0.679626\pi$
$788$		−	2986.06i		−	0.134992i
$789$		0			0
$790$	2020.42	+	3499.47i	0.0909916	+	0.157602i
$791$	−21378.7	+	12343.0i	−0.960984	+	0.554825i
$792$		0			0
$793$	−15218.2	+	15155.1i	−0.681482	+	0.678656i
$794$	−926.524			−0.0414120
$795$		0			0
$796$	5314.59	+	9205.13i	0.236646	+	0.409883i
$797$	17645.3	−	30562.5i	0.784226	−	1.35832i	−0.145234	−	0.989397i	$-0.546393\pi$
$797$	17645.3	−	30562.5i	0.784226	−	1.35832i	0.929460	−	0.368923i	$-0.120273\pi$
$798$		0			0
$799$	47776.5	+	27583.8i	2.11541	+	1.22133i
$800$	3161.16	+	1825.10i	0.139705	+	0.0806586i
$801$		0			0
$802$	14052.6	−	24339.9i	0.618724	−	1.07166i
$803$	−815.690	−	1412.82i	−0.0358469	−	0.0620887i
$804$		0			0
$805$	12901.4			0.564862
$806$	4837.41	+	18204.7i	0.211402	+	0.795574i
$807$		0			0
$808$	6619.92	−	3822.01i	0.288227	−	0.166408i
$809$	9348.92	+	16192.8i	0.406292	+	0.703719i	0.994471	−	0.105012i	$-0.0334881\pi$
$809$	9348.92	+	16192.8i	0.406292	+	0.703719i	−0.588178	+	0.808731i	$0.700155\pi$
$810$		0			0
$811$		−	22245.0i		−	0.963165i	−0.876401	−	0.481582i	$-0.840062\pi$
$811$		−	22245.0i		−	0.963165i	0.876401	−	0.481582i	$-0.159938\pi$
$812$	6328.66	+	3653.85i	0.273513	+	0.157913i
$813$		0			0
$814$			3278.67i			0.141176i
$815$	478.910	−	829.496i	0.0205834	−	0.0356515i
$816$		0			0
$817$	5898.78	−	3405.66i	0.252597	−	0.145837i
$818$	8879.08			0.379523
$819$		0			0
$820$	−2923.82			−0.124517
$821$	34027.2	−	19645.6i	1.44648	−	0.835123i	0.448207	−	0.893930i	$-0.352063\pi$
$821$	34027.2	−	19645.6i	1.44648	−	0.835123i	0.998269	+	0.0588066i	$0.0187295\pi$
$822$		0			0
$823$	15.7571	−	27.2921i	0.000667386	−	0.00115595i	−0.865692	−	0.500578i	$-0.833121\pi$
$823$	15.7571	−	27.2921i	0.000667386	−	0.00115595i	0.866359	+	0.499422i	$0.166454\pi$
$824$		−	11831.7i		−	0.500213i
$825$		0			0
$826$	−30279.8	−	17482.1i	−1.27551	−	0.736415i
$827$			30870.8i			1.29805i	0.760769	+	0.649023i	$0.224822\pi$
$827$			30870.8i			1.29805i	−0.760769	+	0.649023i	$0.775178\pi$
$828$		0			0
$829$	19332.5	+	33484.9i	0.809946	+	1.40287i	0.912901	+	0.408181i	$0.133837\pi$
$829$	19332.5	+	33484.9i	0.809946	+	1.40287i	−0.102955	+	0.994686i	$0.532830\pi$
$830$	2815.02	−	1625.25i	0.117724	−	0.0679680i
$831$		0			0
$832$	2895.98	+	782.430i	0.120673	+	0.0326032i
$833$	69199.6			2.87830
$834$		0			0
$835$	3848.72	+	6666.17i	0.159509	+	0.276278i
$836$	−1897.59	+	3286.72i	−0.0785041	+	0.135973i
$837$		0			0
$838$	23692.8	+	13679.0i	0.976674	+	0.563883i
$839$	−8566.99	−	4946.15i	−0.352521	−	0.203528i	0.313274	−	0.949663i	$-0.398574\pi$
$839$	−8566.99	−	4946.15i	−0.352521	−	0.203528i	−0.665795	+	0.746135i	$0.731908\pi$
$840$		0			0
$841$	10500.9	−	18188.0i	0.430558	−	0.745748i
$842$	−11133.2	−	19283.3i	−0.455673	−	0.789248i
$843$		0			0
$844$	6029.37			0.245900
$845$	3658.07	−	6275.58i	0.148925	−	0.255487i
$846$		0			0
$847$	−29558.3	+	17065.5i	−1.19910	+	0.692299i
$848$	−1774.04	−	3072.73i	−0.0718405	−	0.124431i
$849$		0			0
$850$			24576.7i			0.991733i
$851$	−11305.1	−	6527.03i	−0.455388	−	0.262919i
$852$		0			0
$853$			35366.0i			1.41959i	0.704409	+	0.709794i	$0.251212\pi$
$853$			35366.0i			1.41959i	−0.704409	+	0.709794i	$0.748788\pi$
$854$	−14383.4	+	24912.7i	−0.576333	+	0.998238i
$855$		0			0
$856$	−1476.51	+	852.463i	−0.0589556	+	0.0340381i
$857$	760.177			0.0303001			0.0151500	−	0.999885i	$-0.495177\pi$
$857$	760.177			0.0303001			0.0151500	+	0.999885i	$0.495177\pi$
$858$		0			0
$859$	27332.4			1.08565			0.542823	−	0.839847i	$-0.317355\pi$
$859$	27332.4			1.08565			0.542823	+	0.839847i	$0.317355\pi$
$860$	−1283.55	+	741.057i	−0.0508937	+	0.0293835i
$861$		0			0
$862$	−1454.09	+	2518.55i	−0.0574552	+	0.0995153i
$863$			35583.9i			1.40358i	0.712384	+	0.701790i	$0.247615\pi$
$863$			35583.9i			1.40358i	−0.712384	+	0.701790i	$0.752385\pi$
$864$		0			0
$865$	3046.25	+	1758.75i	0.119740	+	0.0691322i
$866$		−	15377.1i		−	0.603391i
$867$		0			0
$868$	12614.8	+	21849.5i	0.493288	+	0.854400i
$869$	−8261.39	+	4769.72i	−0.322496	+	0.186193i
$870$		0			0
$871$	−23997.3	+	6376.64i	−0.933545	+	0.248065i
$872$	−675.358			−0.0262276
$873$		0			0
$874$	−7555.26	−	13086.1i	−0.292403	−	0.506458i
$875$	12405.9	−	21487.7i	0.479311	−	0.830191i
$876$		0			0
$877$	−2983.50	−	1722.52i	−0.114875	−	0.0663232i	0.441462	−	0.897280i	$-0.354460\pi$
$877$	−2983.50	−	1722.52i	−0.114875	−	0.0663232i	−0.556337	+	0.830957i	$0.687793\pi$
$878$	14967.7	+	8641.61i	0.575325	+	0.332164i
$879$		0			0
$880$	412.907	−	715.175i	0.0158171	−	0.0273961i
$881$	10148.1	+	17577.0i	0.388079	+	0.672173i	0.992191	−	0.124727i	$-0.0398054\pi$
$881$	10148.1	+	17577.0i	0.388079	+	0.672173i	−0.604112	+	0.796899i	$0.706472\pi$
$882$		0			0
$883$	−2952.08			−0.112509			−0.0562545	−	0.998416i	$-0.517916\pi$
$883$	−2952.08			−0.112509			−0.0562545	+	0.998416i	$0.517916\pi$
$884$	5187.00	+	19520.3i	0.197350	+	0.742692i
$885$		0			0
$886$	−23492.9	+	13563.6i	−0.890813	+	0.514311i
$887$	12377.2	+	21438.0i	0.468531	+	0.811520i	0.999353	−	0.0359637i	$-0.0114501\pi$
$887$	12377.2	+	21438.0i	0.468531	+	0.811520i	−0.530822	+	0.847483i	$0.678117\pi$
$888$		0			0
$889$		−	22992.0i		−	0.867411i
$890$	−2159.84	−	1246.98i	−0.0813460	−	0.0469651i
$891$		0			0
$892$		−	7916.23i		−	0.297147i
$893$	−15562.4	+	26954.9i	−0.583176	+	1.01009i
$894$		0			0
$895$	−7075.29	+	4084.92i	−0.264247	+	0.152563i
$896$	4017.97			0.149811
$897$		0			0
$898$	37594.6			1.39705
$899$	−10127.6	+	5847.20i	−0.375724	+	0.216924i
$900$		0			0
$901$	11944.6	−	20688.6i	0.441655	−	0.764969i
$902$		−	6902.42i		−	0.254795i
$903$		0			0
$904$	−5448.47	−	3145.67i	−0.200457	−	0.115734i
$905$			7262.26i			0.266747i
$906$		0			0
$907$	12103.5	+	20963.9i	0.443099	+	0.767469i	0.997918	−	0.0645018i	$-0.0205458\pi$
$907$	12103.5	+	20963.9i	0.443099	+	0.767469i	−0.554819	+	0.831971i	$0.687212\pi$
$908$	7311.99	−	4221.58i	0.267243	−	0.154293i
$909$		0			0
$910$	2537.66	−	9392.55i	0.0924423	−	0.342154i
$911$	21027.3			0.764725			0.382363	−	0.924012i	$-0.375111\pi$
$911$	21027.3			0.764725			0.382363	+	0.924012i	$0.375111\pi$
$912$		0			0
$913$	3836.83	+	6645.58i	0.139080	+	0.240894i
$914$	−7225.60	+	12515.1i	−0.261490	+	0.452913i
$915$		0			0
$916$	−18452.4	−	10653.5i	−0.665595	−	0.384282i
$917$	−50629.3	−	29230.9i	−1.82326	−	1.05266i
$918$		0			0
$919$	3949.78	−	6841.22i	0.141775	−	0.245561i	−0.786390	−	0.617730i	$-0.788052\pi$
$919$	3949.78	−	6841.22i	0.141775	−	0.245561i	0.928165	+	0.372169i	$0.121386\pi$
$920$	1643.99	+	2847.48i	0.0589139	+	0.102042i
$921$		0			0
$922$	4590.72			0.163977
$923$	2234.22	+	2243.53i	0.0796753	+	0.0800072i
$924$		0			0
$925$	−10373.9	+	5989.38i	−0.368748	+	0.212897i
$926$	−9457.75	−	16381.3i	−0.335638	−	0.581342i
$927$		0			0
$928$			1862.41i			0.0658798i
$929$	−4706.55	−	2717.33i	−0.166218	−	0.0959662i	0.414583	−	0.910011i	$-0.363927\pi$
$929$	−4706.55	−	2717.33i	−0.166218	−	0.0959662i	−0.580801	+	0.814045i	$0.697261\pi$
$930$		0			0
$931$			39041.5i			1.37437i
$932$	−297.898	+	515.974i	−0.0104699	+	0.0181344i
$933$		0			0
$934$	23055.2	−	13310.9i	0.807696	−	0.466323i
$935$	5560.19			0.194479
$936$		0			0
$937$	8130.03			0.283454			0.141727	−	0.989906i	$-0.454734\pi$
$937$	8130.03			0.283454			0.141727	+	0.989906i	$0.454734\pi$
$938$	−28801.8	+	16628.8i	−1.00257	+	0.578836i
$939$		0			0
$940$	3386.31	−	5865.27i	0.117499	−	0.203515i
$941$			5409.95i			0.187417i	0.995600	+	0.0937084i	$0.0298721\pi$
$941$			5409.95i			0.187417i	−0.995600	+	0.0937084i	$0.970128\pi$
$942$		0			0
$943$	23800.2	+	13741.0i	0.821887	+	0.474517i
$944$		−	8910.79i		−	0.307226i
$945$		0			0
$946$	−1749.45	−	3030.14i	−0.0601264	−	0.104142i
$947$	−32164.9	+	18570.4i	−1.10372	+	0.637231i	−0.937195	−	0.348807i	$-0.886587\pi$
$947$	−32164.9	+	18570.4i	−1.10372	+	0.637231i	−0.166522	+	0.986038i	$0.553254\pi$
$948$		0			0
$949$	1277.61	−	4728.79i	0.0437018	−	0.161752i
$950$	−13865.8			−0.473544
$951$		0			0
$952$	13526.5	+	23428.5i	0.460499	+	0.797608i
$953$	1770.71	−	3066.97i	0.0601879	−	0.104249i	−0.834361	−	0.551218i	$-0.814163\pi$
$953$	1770.71	−	3066.97i	0.0601879	−	0.104249i	0.894549	+	0.446969i	$0.147497\pi$
$954$		0			0
$955$	−5873.27	−	3390.93i	−0.199010	−	0.114899i
$956$	−10673.5	−	6162.36i	−0.361095	−	0.208478i
$957$		0			0
$958$	−7969.25	+	13803.1i	−0.268763	+	0.465511i
$959$	13928.8	+	24125.4i	0.469014	+	0.812356i
$960$		0			0
$961$	−10583.5			−0.355258
$962$	−6975.53	+	6946.60i	−0.233784	+	0.232814i
$963$		0			0
$964$	8903.76	−	5140.59i	0.297480	−	0.171750i
$965$	−6204.48	−	10746.5i	−0.206974	−	0.358489i
$966$		0			0
$967$			48102.4i			1.59966i	0.600229	+	0.799828i	$0.295076\pi$
$967$			48102.4i			1.59966i	−0.600229	+	0.799828i	$0.704924\pi$
$968$	−7533.09	−	4349.23i	−0.250127	−	0.144411i
$969$		0			0
$970$		−	3791.07i		−	0.125488i
$971$	17539.6	−	30379.5i	0.579683	−	1.00404i	−0.415833	−	0.909441i	$-0.636510\pi$
$971$	17539.6	−	30379.5i	0.579683	−	1.00404i	0.995515	−	0.0945990i	$-0.0301569\pi$
$972$		0			0
$973$	39475.7	−	22791.3i	1.30065	−	0.750931i
$974$	2830.94			0.0931305
$975$		0			0
$976$	−7331.35			−0.240441
$977$	36950.2	−	21333.2i	1.20997	−	0.698577i	0.247217	−	0.968960i	$-0.420484\pi$
$977$	36950.2	−	21333.2i	1.20997	−	0.698577i	0.962753	+	0.270383i	$0.0871505\pi$
$978$		0			0
$979$	2943.82	−	5098.85i	0.0961031	−	0.166455i
$980$		−	8495.26i		−	0.276909i
$981$		0			0
$982$	−5544.15	−	3200.91i	−0.180164	−	0.104018i
$983$			32297.0i			1.04793i	0.851740	+	0.523964i	$0.175547\pi$
$983$			32297.0i			1.04793i	−0.851740	+	0.523964i	$0.824453\pi$
$984$		0			0
$985$	−1234.10	−	2137.52i	−0.0399204	−	0.0691442i
$986$	−10859.6	+	6269.77i	−0.350749	+	0.202505i
$987$		0			0
$988$	−11013.1	+	2926.44i	−0.354629	+	0.0942332i
$989$	13930.9			0.447905
$990$		0			0
$991$	5674.60	+	9828.69i	0.181897	+	0.315054i	0.942526	−	0.334132i	$-0.108443\pi$
$991$	5674.60	+	9828.69i	0.181897	+	0.315054i	−0.760630	+	0.649186i	$0.775110\pi$
$992$	−3214.94	+	5568.45i	−0.102898	+	0.178224i
$993$		0			0
$994$	3672.72	+	2120.45i	0.117195	+	0.0676625i
$995$	7608.70	+	4392.89i	0.242424	+	0.139964i
$996$		0			0
$997$	15268.2	−	26445.3i	0.485003	−	0.840050i	−0.514848	−	0.857281i	$-0.672152\pi$
$997$	15268.2	−	26445.3i	0.485003	−	0.840050i	0.999852	+	0.0172310i	$0.00548508\pi$
$998$	1480.51	+	2564.32i	0.0469588	+	0.0813349i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	234.4.l.b.127.1		8
3.2	odd	2		26.4.e.a.23.3	yes	8
12.11	even	2		208.4.w.d.49.4		8
13.4	even	6	inner	234.4.l.b.199.2		8
39.2	even	12		338.4.a.m.1.4		4
39.5	even	4		338.4.c.m.315.1		8
39.8	even	4		338.4.c.n.315.1		8
39.11	even	12		338.4.a.l.1.4		4
39.17	odd	6		26.4.e.a.17.3	✓	8
39.20	even	12		338.4.c.n.191.1		8
39.23	odd	6		338.4.b.g.337.4		8
39.29	odd	6		338.4.b.g.337.8		8
39.32	even	12		338.4.c.m.191.1		8
39.35	odd	6		338.4.e.e.147.1		8
39.38	odd	2		338.4.e.e.23.1		8
156.95	even	6		208.4.w.d.17.4		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
26.4.e.a.17.3	✓	8	39.17	odd	6
26.4.e.a.23.3	yes	8	3.2	odd	2
208.4.w.d.17.4		8	156.95	even	6
208.4.w.d.49.4		8	12.11	even	2
234.4.l.b.127.1		8	1.1	even	1	trivial
234.4.l.b.199.2		8	13.4	even	6	inner
338.4.a.l.1.4		4	39.11	even	12
338.4.a.m.1.4		4	39.2	even	12
338.4.b.g.337.4		8	39.23	odd	6
338.4.b.g.337.8		8	39.29	odd	6
338.4.c.m.191.1		8	39.32	even	12
338.4.c.m.315.1		8	39.5	even	4
338.4.c.n.191.1		8	39.20	even	12
338.4.c.n.315.1		8	39.8	even	4
338.4.e.e.23.1		8	39.38	odd	2
338.4.e.e.147.1		8	39.35	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 234 = 2 \cdot 3^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	234.l (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.73205 + 1.00000i) q^{2} +(2.00000 - 3.46410i) q^{4} -3.30629i q^{5} +(27.1849 + 15.6952i) q^{7} +8.00000i q^{8} +O(q^{10})\)	\(q+(-1.73205 + 1.00000i) q^{2} +(2.00000 - 3.46410i) q^{4} -3.30629i q^{5} +(27.1849 + 15.6952i) q^{7} +8.00000i q^{8} +(3.30629 + 5.72666i) q^{10} +(-13.5192 + 7.80533i) q^{11} +(-45.2497 - 12.2255i) q^{13} -62.7808 q^{14} +(-8.00000 - 13.8564i) q^{16} +(53.8638 - 93.2949i) q^{17} +(52.6358 + 30.3893i) q^{19} +(-11.4533 - 6.61258i) q^{20} +(15.6107 - 27.0385i) q^{22} +(62.1540 + 107.654i) q^{23} +114.068 q^{25} +(90.6003 - 24.0746i) q^{26} +(108.740 - 62.7808i) q^{28} +(29.1001 + 50.4028i) q^{29} +200.934i q^{31} +(27.7128 + 16.0000i) q^{32} +215.455i q^{34} +(51.8928 - 89.8810i) q^{35} +(-90.9447 + 52.5069i) q^{37} -121.557 q^{38} +26.4503 q^{40} +(191.461 - 110.540i) q^{41} +(56.0339 - 97.0535i) q^{43} +62.4426i q^{44} +(-215.308 - 124.308i) q^{46} +512.102i q^{47} +(321.178 + 556.297i) q^{49} +(-197.572 + 114.068i) q^{50} +(-132.850 + 132.299i) q^{52} +221.755 q^{53} +(25.8067 + 44.6985i) q^{55} +(-125.562 + 217.479i) q^{56} +(-100.806 - 58.2002i) q^{58} +(482.310 + 278.462i) q^{59} +(229.105 - 396.821i) q^{61} +(-200.934 - 348.028i) q^{62} -64.0000 q^{64} +(-40.4209 + 149.609i) q^{65} +(458.769 - 264.870i) q^{67} +(-215.455 - 373.180i) q^{68} +207.571i q^{70} +(-58.5007 - 33.7754i) q^{71} +104.504i q^{73} +(105.014 - 181.889i) q^{74} +(210.543 - 121.557i) q^{76} -490.025 q^{77} +611.085 q^{79} +(-45.8133 + 26.4503i) q^{80} +(-221.080 + 382.922i) q^{82} -491.565i q^{83} +(-308.460 - 178.089i) q^{85} +224.136i q^{86} +(-62.4426 - 108.154i) q^{88} +(-326.626 + 188.578i) q^{89} +(-1038.23 - 1042.55i) q^{91} +497.232 q^{92} +(-512.102 - 886.987i) q^{94} +(100.476 - 174.029i) q^{95} +(-496.503 - 286.656i) q^{97} +(-1112.59 - 642.357i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 16 q^{4} + 18 q^{7}+O(q^{10}) \) 8 * q + 16 * q^4 + 18 * q^7	\( 8 q + 16 q^{4} + 18 q^{7} - 8 q^{10} + 18 q^{11} - 130 q^{13} - 80 q^{14} - 64 q^{16} - 112 q^{17} + 594 q^{19} - 72 q^{20} - 72 q^{22} + 230 q^{23} - 180 q^{25} + 184 q^{26} + 72 q^{28} - 32 q^{29} + 128 q^{35} - 768 q^{37} + 576 q^{38} - 64 q^{40} + 564 q^{41} - 114 q^{43} + 576 q^{46} - 110 q^{49} - 1968 q^{50} - 104 q^{52} - 36 q^{53} + 1248 q^{55} - 160 q^{56} - 1848 q^{58} + 1110 q^{59} + 900 q^{61} - 1064 q^{62} - 512 q^{64} - 1870 q^{65} + 510 q^{67} + 448 q^{68} + 1470 q^{71} + 680 q^{74} + 2376 q^{76} - 2340 q^{77} + 784 q^{79} - 288 q^{80} + 704 q^{82} - 2898 q^{85} + 288 q^{88} + 4434 q^{89} - 886 q^{91} + 1840 q^{92} - 2568 q^{94} + 816 q^{95} + 1854 q^{97} - 4272 q^{98}+O(q^{100}) \) 8 * q + 16 * q^4 + 18 * q^7 - 8 * q^10 + 18 * q^11 - 130 * q^13 - 80 * q^14 - 64 * q^16 - 112 * q^17 + 594 * q^19 - 72 * q^20 - 72 * q^22 + 230 * q^23 - 180 * q^25 + 184 * q^26 + 72 * q^28 - 32 * q^29 + 128 * q^35 - 768 * q^37 + 576 * q^38 - 64 * q^40 + 564 * q^41 - 114 * q^43 + 576 * q^46 - 110 * q^49 - 1968 * q^50 - 104 * q^52 - 36 * q^53 + 1248 * q^55 - 160 * q^56 - 1848 * q^58 + 1110 * q^59 + 900 * q^61 - 1064 * q^62 - 512 * q^64 - 1870 * q^65 + 510 * q^67 + 448 * q^68 + 1470 * q^71 + 680 * q^74 + 2376 * q^76 - 2340 * q^77 + 784 * q^79 - 288 * q^80 + 704 * q^82 - 2898 * q^85 + 288 * q^88 + 4434 * q^89 - 886 * q^91 + 1840 * q^92 - 2568 * q^94 + 816 * q^95 + 1854 * q^97 - 4272 * q^98

Introduction

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